Given the above definitions for torsion and non-metricity one can easily show (see for instance [1]}) the affine connection decompositionFrom here onwards we shall use the tilde notation in order to denote Riemannian objects, that is objects computed with respect to the Levi-Civita connection \(\tilde{\Gamma }^{\lambda }_{\;\;\;\mu \nu }\) .
\(\Gamma ^{\lambda }_{\;\;\;\mu \nu }=N^{\lambda }_{\;\;\;\;\mu \nu }+\tilde{\Gamma }^{\lambda }_{\;\;\;\mu \nu }=\frac{1}{2}g^{\alpha \lambda }(Q_{\mu \nu \alpha }+Q_{\nu \alpha \mu }-Q_{\alpha \mu \nu }) -g^{\alpha \lambda }(S_{\alpha \mu \nu }+S_{\alpha \nu \mu }-S_{\mu \nu \alpha }) \) 
